The half-life of radioactive substance is 2.5 minutes. what fraction of the origional radioactive remains after 10 mins

The answer is 1/16.

Half-life is the time required for the amount of a sample to half its value.
To calculate this, we will use the following formulas:
1. ,
where:
n - a number of half-lives
x - a remained fraction of a sample

2. 
where:
- half-life
t - total time elapsed
n - a number of half-lives

So, we know:
t = 10 min
= 2.5 min

We need:
n = ?
x = ?

We could first use the second equation to calculate n:
If:
,
Then: 

⇒ 
⇒ 

Now we can use the first equation to calculate the remained fraction of the sample.

⇒ 
⇒

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